Apply all relevant Properties of Exponents to simplify the following expressio completely. a) \( \left(-8 x^{2} n^{6}\right)^{3} \)

To simplify \( \left(-8 x^{2} n^{6}\right)^{3} \), we apply the power of a product property. This means we raise each factor to the exponent of 3. Calculating this, we get: \[ (-8)^{3} \cdot (x^{2})^{3} \cdot (n^{6})^{3} = -512 \cdot x^{6} \cdot n^{18}. \] Thus, the fully simplified expression is \( -512 x^{6} n^{18} \). For a little fun refresher: remember, negative bases raised to an odd power (like 3) stay negative, which is why we ended up with -512! Keep that in mind if you're mixing signs in future problems!